Related to bvp4c matlab code

Dear experts,

Anyone help me,

how to plot isotherm lines, contour plot, surface plot using matlab bvp4c.

suggests any sample codes or any ideas.

Thank you.

this is our code

function hybrid(solver)

if nargin < 1

solver = 'bvp4c';

end

bvpsolver = fcnchk(solver);

xlow=0;

g1=-1;

g2=1;

g3=0.5;

g4=0.5;

global St rad m

St=0.2;

infinity=01;

maxinfinity=15;

solinit=bvpinit(linspace(0,infinity,1001),[St g1 1 g2 0 1 g3 1 g4]);

sol = bvpsolver(@ode,@bc,solinit);

x = sol.x;

y = sol.y;

fprintf('\n');

fprintf('At eta= %g \t %10.8f \t %10.8f \t %10.8f %10.8f.\n',xlow,y(2,1),y(4,1),y(7,1),y(9,1))

for Bnew = infinity:01:maxinfinity

solinit = bvpxtend(sol,Bnew);

sol = bvpsolver(@ode,@bc,solinit);

x = sol.x;

y = sol.y;

fprintf('At eta= %g \t %10.8f \t %10.8f \t %10.8f %10.8f.\n',Bnew,y(2,1),y(4,1),y(7,1),y(9,1))

end

fprintf('%10.8f \t %10.8f \t %10.8f \t %10.8f.\n',y(2,1),y(4,1),y(7,1),y(9,1))

plot(x,y(6,:),'-','Linewidth',1.5)

% hold on

%Cf=rad*(1+rad)^m*((0.32906655)^2+(-1.12865255)^2)^(1/2)

%Nu=-rad*(1+rad)^m*y(7);

%Sh=-rad*(1+rad)^m*y(9)

%Sn=-rad*(1+rad)^m*y(11)

function dydx=ode(x,y)

% rhos1 = 2810; Cps1 = 960; ks1 = 173; Pi1 = 0.1; ss1 = 26.77*(10^6); %AA7075

% rhos2 = 2720; Cps2 = 893.2; ks2 = 222; Pi2 = 0.3; ss2 = 34.83*(10^6); %AA7072

% rhof = 792; Cpf = 2545; kf = 0.2035; sf = 0.5*(10^(-6)); %(Methonal)

Np=2;

alpha=0.15;

eps=0.45;

Re=1;

Pr=1.5;

rad=0.2;

m=1.1;

n=0.1;

Sc=01;

Beta=1;

B=1;

Ha=0.2;

Ec=0.1;

Del=0.01;

h=0.5;

Rp=1.5;

% knf = kf*(ks1+(Np-1)*kf-(Np-1)*Pi1*(kf-ks1))/(ks1+(Np-1)*kf+Pi1*(kf-ks1));

% K =(ks2+(Np-1)*knf+Pi2*(knf-ks2)) /(ks2+(Np-1)*knf-(Np-1)*Pi2*(knf-ks2));%khnf/kf

%

% snf = sf*(ss1+2*sf-2*Pi1*(sf-ss1))/(ss1+2*sf+Pi1*(sf-ss1));

% S = (ss2+2*snf-2*Pi2*(snf-ss2))/(ss2+2*snf+Pi2*(snf-ss2));%shnf/sf

%

% Rh=(1-Pi2)*((1-Pi1)+Pi1*((rhos1*Cps1)/(rhof*Cpf)))+Pi2*((rhos2*Cps2)/(rhof*Cpf));

% Mu=1/((1-Pi1)^(2.5)*(1-Pi2)^(2.5));

% D=1.8;

% RaggRp=3.34;

% Pmax=0.605;

% Pint=(RaggRp)^(D-3);

% Pagg=Pi/Pint;

% rhoagg=(1-Pint)*rhof+Pint*rhos;

% Mu=(1/(Pagg/Pmax))^(-2.5*Pmax);

% Rh=(1-Pagg)+((Pagg*rhoagg)/rhof);

% rhoCpagg=(1-Pint)*(rhof*Cpf)+Pint*rhos*Cps;

% kagg=(kf/4)*((3*Pint-1)*(ks/kf)+(3*(1-Pint)-1)+(((3*Pint-1)*(ks/kf)+(3*(1-Pint)-1))^2+(8*ks/kf))^0.5);

% RhCp=(1-Pagg)+Pagg*(rhoCpagg/(rhof*Cpf));

% K=(kagg+2*kf+2*Pagg*(kagg-kf))/(kagg+2*kf-Pagg*(kagg-kf));

% S=1+(((3*(ss/sf)-1)*Pagg)/((ss/sf)+2)*((ss/sf)-1)*Pagg);

rhos = 2810; Cps = 960; ks = 173; Pi = 0.1; ss = 26.77*(10^6); %AA7075

rhof = 792; Cpf = 2545; kf = 0.2035; sf = 0.5*(10^(-6)); %(Methonal)

Mu=1+2.5*Del+4.5*(1/((h/Rp)*(2+(h/Rp))*(1+(h/Rp))^2));

Rh=(1-Del)+Del*(rhos/rhof);

RhCp=(1-Del)+Del*(rhos*Cps/rhof*Cpf);

K=(ks+2*kf-2*Del*(kf-ks))/(ks+2*kf+Del*(kf-ks));

S=(ss+2*sf-2*Del*(sf-ss))/(ss+2*sf+Del*(sf-ss));

dydx=[y(2)

Rh*(y(1)^2-y(3)^2+m*eps*(x+alpha)*y(1)*y(2)+y(5)*y(2))-(B/Re^2)+S*Ha*y(1)/Mu*Re^((1-n)/(1+n))*(1+rad)^(2*m)*(1+(1/Beta))

y(4)

Rh*(2*y(1)*y(3)+y(5)*y(4)+m*eps*(x+alpha)*y(1)*y(4))+S*Ha*y(3)/Mu*Re^((1-n)/(1+n))*(1+rad)^(2*m)*(1+(1/Beta))

-2*y(1)-m*eps*(x+alpha)*y(2)

y(7)

(y(1)*y(7)*m*eps*(x+alpha)*Pr+Pr*y(5)*y(7)+Pr*(S*RhCp)*Ha*Ec*(y(1)^2+y(3)^2))/(K*RhCp)*Re^((1-n)/(1+n))*(1+rad)^(2*m)

y(9)

(Sc*y(1)*y(9)*m*eps*(x+alpha)+Sc*y(5)*y(9))/(Mu*Re^((1-n)/(1+n))*(1+rad)^(2*m))

];

end

function res=bc(y0,yinf)

res=[y0(1)-St

y0(3)-1

y0(5)

y0(6)-1

y0(8)-1

yinf(1)

yinf(3)

yinf(6)

yinf(8)

];

end

end

Answer 1

[Syed Sohaib Zafar]

I think You need these kind of graphs.

To plot such graphs, use the command "contourf".

Find more help from the link below.

https://www.mathworks.com/help/matlab/ref/contourf.html